The value of multichannel MEG and EEG in the presurgical evaluation of 70 epilepsy patients

OBJECTIVE

To evaluate the sensitivity of a simultaneous whole-head 306-channel magnetoencephalography (MEG)/70-electrode EEG recording to detect interictal epileptiform activity (IED) in a prospective, consecutive cohort of patients with medically refractory epilepsy that were considered candidates for epilepsy surgery.

METHODS

Seventy patients were prospectively evaluated by simultaneously recorded MEG/EEG. All patients were surgical candidates or were considered for invasive EEG monitoring and had undergone an extensive presurgical evaluation at a tertiary epilepsy center. MEG and EEG raw traces were analysed individually by two independent reviewers.

RESULTS

MEG data could not be evaluated due to excessive magnetic artefacts in three patients (4%). In the remaining 67 patients, the overall sensitivity to detect IED was 72% (48/67 patients) for MEG and 61% for EEG (41/67 patients) analysing the raw data. In 13% (9/67 patients), MEG-only IED were recorded, whereas in 3% (2/67 patients) EEG-only IED were recorded. The combined sensitivity was 75% (50/67 patients).

CONCLUSION

Three hundred and six-channel MEG has a similarly high sensitivity to record IED as EEG and appears to be complementary. In one-third of the EEG-negative patients, MEG can be expected to record IED, especially in the case of lateral neocortical epilepsy and/or cortical dysplasia.

Top-down facilitation of visual recognition

Cortical analysis related to visual object recognition is traditionally thought to propagate serially along a bottom-up hierarchy of ventral areas. Recent proposals gradually promote the role of top-down processing in recognition, but how such facilitation is triggered remains a puzzle. We tested a specific model, proposing that low spatial frequencies facilitate visual object recognition by initiating top-down processes projected from orbitofrontal to visual cortex. The present study combined magnetoencephalography, which has superior temporal resolution, functional magnetic resonance imaging, and a behavioral task that yields successful recognition with stimulus repetitions. Object recognition elicited differential activity that developed in the left orbitofrontal cortex 50 ms earlier than it did in recognition-related areas in the temporal cortex. This early orbitofrontal activity was directly modulated by the presence of low spatial frequencies in the image. Taken together, the dynamics we revealed provide strong support for the proposal of how top-down facilitation of object recognition is initiated, and our observations are used to derive predictions for future research.

3T phased array MRI improves the presurgical evaluation in focal epilepsies: A prospective study

BACKGROUND

Although detection of concordant lesions on MRI significantly improves postsurgical outcomes in focal epilepsy (FE), many conventional MR studies remain negative. The authors evaluated the role of phased array surface coil studies performed at 3 Tesla (3T PA MRI).

METHODS

Forty patients with medically intractable focal epilepsies were prospectively imaged with 3T PA-MRI including high matrix TSE T2, fluid attenuated inversion recovery, and magnetization prepared rapid gradient echo. All patients were considered candidates for epilepsy surgery. 3T PA-MRIs were reviewed by a neuroradiologist experienced in epilepsy imaging with access to clinical information. Findings were compared to reports of prior standard 1.5T MRI epilepsy studies performed at tertiary care centers.

RESULTS

Experienced, unblinded review of 3T PA-MRI studies yielded additional diagnostic information in 48% (19/40) compared to routine clinical reads at 1.5T. In 37.5% (15/40), this additional information motivated a change in clinical management. In the subgroup of patients with prior 1.5T MRIs interpreted as normal, 3T PA-MRI resulted in the detection of a new lesion in 65% (15/23). In the subgroup of 15 patients with known lesions, 3T PA-MRI better defined the lesion in 33% (5/15).

CONCLUSION

Phased array surface coil studies performed at 3 Tesla read by an experienced unblinded neuroradiologist can improve the presurgical evaluation of patients with focal epilepsy when compared to routine clinical 1.5T studies read at tertiary care centers.

Cerebral cortex thickness in 15-year-old adolescents with low birth weight measured by an automated MRI-based method

Infants with low birth weight are at increased risk of perinatal brain injury. Disruption of normal cortical development may have consequences for later motor, behavioural and cognitive development. The aim of this study was to measure cerebral cortical thickness, area and volume with an automated MRI technique in 15-year-old adolescents who had low birth weight. Cerebral MRI for morphometric analysis was performed on 50 very low birth weight (VLBW, birth weight </=1500 g), 49 term small for gestational age births (SGA, birth weight <10th percentile at term) and 58 control adolescents. A novel method of cortical surface models yielded measurements of cortical thickness and area for each subject's entire brain and computed cross-subject statistics based on cortical anatomy. The cortical surface models demonstrated regional thinning of the parietal, temporal and occipital lobes in the VLBW group, whereas regional thickening was demonstrated in the frontal and occipital lobes. The areas of change were greatest in those with the shortest gestational age at birth and lowest birth weight. Cortical surface area and cortical volume were lower in the VLBW than in the Control group. Within the VLBW group, there was an association between surface area and estimation of the intelligence quotient IQ (IQ(est)) and between cortical volume and IQ(est). Furthermore, cortical grey matter as a proportion of brain volume was significantly lower in the VLBW, but not in the SGA group compared with Controls. This observed reorganization of the developing brain offers a unique opportunity to investigate any relationship between changes in cortical anatomy and cognitive and social impairments, and the increase in psychiatric disorders that have been found in VLBW children and adolescents.

Size does matter in the long run: hippocampal and cortical volume predict recall across weeks

OBJECTIVE

To study the morphometric determinants of recall of verbal material for an extended period in an adult lifespan sample.

METHODS

Healthy adults of varying ages were studied using automated segmentation of MRI scans with volumes of hippocampus, cortex, and white matter, and verbal memory tests assessing recall after 5 minutes, 30 minutes, and a mean period of 11 weeks. Stepwise regression analyses were performed with 5 minutes, 30 minutes, and 11-week recall as the dependent variables. Hippocampal, cortical, and white matter volumes were included in the initial set of predictor variables in each case, and the analyses were repeated with age as an additional predictor variable.

RESULTS

When age was not included, cortical volume was the only variable predicting recall after 5 and 30 minutes, whereas hippocampal and cortical volumes predicted recall after 11 weeks. When age was included in the model, this was the only variable predicting recall after 5 and 30 minutes, whereas age and hippocampus gave contributions in prediction of recall after several weeks.

CONCLUSION

This study supports a critical role of cortical and hippocampal size in recall. Hippocampal size seems more important in recall after 11 weeks than after a shorter time interval.

Age-related alterations in white matter microstructure measured by diffusion tensor imaging

Cerebral white matter (WM) undergoes various degenerative changes with normal aging, including decreases in myelin density and alterations in myelin structure. We acquired whole-head, high-resolution diffusion tensor images (DTI) in 38 participants across the adult age span. Maps of fractional anisotropy (FA), a measure of WM microstructure, were calculated for each participant to determine whether particular fiber systems of the brain are preferentially vulnerable to WM degeneration. Regional FA measures were estimated from nine regions of interest in each hemisphere and from the genu and splenium of the corpus callosum (CC). The results showed significant age-related decline in FA in frontal WM, the posterior limb of the internal capsule (PLIC), and the genu of the CC. In contrast, temporal and posterior WM was relatively preserved. These findings suggest that WM alterations are variable throughout the brain and that particular fiber populations within prefrontal region and PLIC are most vulnerable to age-related degeneration.

A hybrid approach to the skull stripping problem in MRI

We present a novel skull-stripping algorithm based on a hybrid approach that combines watershed algorithms and deformable surface models. Our method takes advantage of the robustness of the former as well as the surface information available to the latter. The algorithm first localizes a single white matter voxel in a T1-weighted MRI image, and uses it to create a global minimum in the white matter before applying a watershed algorithm with a preflooding height. The watershed algorithm builds an initial estimate of the brain volume based on the three-dimensional connectivity of the white matter. This first step is robust, and performs well in the presence of intensity nonuniformities and noise, but may erode parts of the cortex that abut bright nonbrain structures such as the eye sockets, or may remove parts of the cerebellum. To correct these inaccuracies, a surface deformation process fits a smooth surface to the masked volume, allowing the incorporation of geometric constraints into the skull-stripping procedure. A statistical atlas, generated from a set of accurately segmented brains, is used to validate and potentially correct the segmentation, and the MRI intensity values are locally re-estimated at the boundary of the brain. Finally, a high-resolution surface deformation is performed that accurately matches the outer boundary of the brain, resulting in a robust and automated procedure. Studies by our group and others outperform other publicly available skull-stripping tools.

Regional and progressive thinning of the cortical ribbon in Huntington's disease

BACKGROUND

Huntington's disease (HD) is a fatal and progressive neurodegenerative disease that is accompanied by involuntary movements, cognitive dysfunction, and psychiatric symptoms. Although progressive striatal degeneration is known to occur, little is known about how the disease affects the cortex, including which cortical regions are affected, how degeneration proceeds, and the relationship of the cortical degeneration to clinical symptoms. The cortex has been difficult to study in neurodegenerative diseases primarily because of its complex folding patterns and regional variability; however, an understanding of how the cortex is affected by the disease may provide important new insights into it.

METHODS

Novel automated surface reconstruction and high-resolution MR images of 11 patients with HD and 13 age-matched subjects were used to obtain cortical thickness measurements. The same analyses were performed on two postmortem brains to validate these methods.

RESULTS

Regionally specific heterogeneous thinning of the cortical ribbon was found in subjects with HD. Thinning occurred early, differed among patients in different clinical stages of disease, and appeared to proceed from posterior to anterior cortical regions with disease progression. The sensorimotor region was statistically most affected. Measurements performed on MR images of autopsy brains analyzed similarly were within 0.25 mm of those obtained using traditional neuropathologic methods and were statistically indistinguishable.

CONCLUSIONS

The authors propose that the cortex degenerates early in disease and that regionally selective cortical degeneration may explain the heterogeneity of clinical expression in HD. These measures might provide a sensitive prospective surrogate marker for clinical trials of neuroprotective medications.

Conductivity tensor mapping of the human brain using diffusion tensor MRI

Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, final sigma and d) in agreement with theoretical bounds and experimental measurements presented here (final sigma/d approximately 0.844 +/- 0.0545 S small middle dots/mm(3), r(2) = 0.945). The extension to other biological transport phenomena is also discussed.

Deconvolution of event-related fMRI responses in fast-rate experimental designs: tracking amplitude variations

Recent developments towards event-related functional magnetic resonance imaging has greatly extended the range of experimental designs. If the events occur in rapid succession, the corresponding time-locked responses overlap significantly and need to be deconvolved in order to separate the contributions of different events. Here we present a deconvolution approach, which is especially aimed at the analysis of fMRI data where sequence- or context-related responses are expected. For this purpose, we make the assumption of a hemodynamic response function (HDR) with constant yet not predefined shape but with possibly variable amplitudes. This approach reduces the number of variables to be estimated but still keeps the solutions flexible with respect to the shape. Consequently, statistical efficiency is improved. Temporal variations of the HDR strength are directly indicated by the amplitudes derived by the algorithm. Both the estimation efficiency and statistical inference are further supported by an improved estimation of the noise covariance. Using synthesized data sets, both differently shaped HDRs and varying amplitude factors were correctly identified. The gain in statistical sensitivity led to improved ratios of false- and true-positive detection rates for synthetic activations in these data. In an event-related fMRI experiment with a human subject, different HDR amplitudes could be derived corresponding to stimulation at different visual stimulus contrasts. Finally, in a visual spatial attention experiment we obtained different fMRI response amplitudes depending on the sequences of attention conditions.

Spatiotemporal Brain Imaging of Visual-Evoked Activity Using Interleaved EEG and fMRI Recordings

Combined analysis of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) has the potential to provide higher spatiotemporal resolution than either method alone. In some situations, in which the activity of interest cannot be reliably reproduced (e.g., epilepsy, learning, sleep states), accurate combined analysis requires simultaneous acquisition of EEG and fMRI. Simultaneous measurements ensure that the EEG and fMRI recordings reflect the exact same brain activity state. We took advantage of the spatial filtering properties of the bipolar montage to allow recording of very short (125--250 ms) visual-evoked potentials (VEPs) during fMRI. These EEG and fMRI measurements are of sufficient quality to allow source localization of the cortical generators. In addition, our source localization approach provides a combined EEG/fMRI analysis that does not require any manual selection of fMRI activations or placement of source dipoles. The source of the VEP was found to be located in the occipital cortex. Separate analysis of EEG and fMRI data demonstrated good spatial overlap of the observed activated sites. As expected, the combined EEG/fMRI analysis provided better spatiotemporal resolution than either approach alone. The resulting spatiotemporal movie allows for the millisecond-to-millisecond display of changes in cortical activity caused by visual stimulation. These data reveal two peaks in activity corresponding to the N75 and the P100 components. This type of simultaneous acquisition and analysis allows for the accurate characterization of the location and timing of neurophysiological activity in the human brain.

Spatiotemporal maps of brain activity underlying word generation and their modification during repetition priming

Spatiotemporal maps of brain activity based on magnetoencephalography were used to observe sequential stages in language processing and their modification during repetition priming. Subjects performed word-stem completion and produced either novel or repeated (primed) words across trials. Activation passes from primary visual cortex (activated at approximately 100 msec after word presentation), to left anteroventral occipital ( approximately 180 msec), to cortex in and near Wernicke's ( approximately 210 msec) and then Broca's ( approximately 370 msec) areas. In addition, a posteroventral temporal area is activated simultaneously with posterosuperior temporal cortex. This area shows an early ( approximately 200-245 msec) increase in activation to repeated word stems. In contrast, prefrontal and anterior temporal regions showed activity reductions to repeated word stems late ( approximately 365-500 msec) in processing. These results tend to support classical models of language and suggest that an effect of direct item repetition is to allow word-form processing to increase its contribution to task performance while concurrently allowing reductions in time-consuming frontal temporal processing.

Spatiotemporal mapping of brain activity by integration of multiple imaging modalities

Functional magnetic resonance imaging (fMRI) and positron emission tomography measure local changes in brain hemodynamics induced by cognitive or perceptual tasks. These measures have a uniformly high spatial resolution of millimeters or less, but poor temporal resolution (about 1s). Conversely, electroencephalography (EEG) and magnetoencephalography (MEG) measure instantaneously the current flows induced by synaptic activity, but the accurate localization of these current flows based on EEG and MEG data alone remains an unsolved problem. Recently, techniques have been developed that, in the context of brain anatomy visualized with structural MRI, use both hemodynamic and electromagnetic measures to arrive at estimates of brain activation with high spatial and temporal resolution. These methods range from simple juxtaposition to simultaneous integrated techniques. Their application has already led to advances in our understanding of the neural bases of perception, attention, memory and language. Further advances in multi-modality integration will require an improved understanding of the coupling between the physiological phenomena underlying the different signal modalities.

Local and global attention are mapped retinotopically in human occipital cortex

Clinical evidence suggests that control mechanisms for local and global attention are lateralized in the temporal-parietal cortex. However, in the human occipital (visual) cortex, the evidence for lateralized local/global attention is controversial. To clarify this matter, we used functional MRI to map activity in the human occipital cortex, during local and global attention, with sustained visual fixation. Data were analyzed in a flattened cortical format, relative to maps of retinotopy and spatial frequency peak tuning. Neither local nor global attention was lateralized in the occipital cortex. Instead, local attention and global attention appear to be special cases of visual spatial attention, which are mapped consistently with the maps of retinotopy and spatial frequency tuning, in multiple visual cortical areas.

Cortical mechanisms specific to explicit visual object recognition

The cortical mechanisms associated with conscious object recognition were studied using functional magnetic resonance imaging (fMRI). Participants were required to recognize pictures of masked objects that were presented very briefly, randomly and repeatedly. This design yielded a gradual accomplishment of successful recognition. Cortical activity in a ventrotemporal visual region was linearly correlated with perception of object identity. Therefore, although object recognition is rapid, awareness of an object's identity is not a discrete phenomenon but rather associated with gradually increasing cortical activity. Furthermore, the focus of the activity in the temporal cortex shifted anteriorly as subjects reported an increased knowledge regarding identity. The results presented here provide new insights into the processes underlying explicit object recognition, as well as the analysis that takes place immediately before and after recognition is possible.

Automated manifold surgery: constructing geometrically accurate and topologically correct models of the human cerebral cortex

Highly accurate surface models of the cerebral cortex are becoming increasingly important as tools in the investigation of the functional organization of the human brain. The construction of such models is difficult using current neuroimaging technology due to the high degree of cortical folding. Even single voxel misclassifications can result in erroneous connections being created between adjacent banks of a sulcus, resulting in a topologically inaccurate model. These topological defects cause the cortical model to no longer be homeomorphic to a sheet, preventing the accurate inflation, flattening, or spherical morphing of the reconstructed cortex. Surface deformation techniques can guarantee the topological correctness of a model, but are time-consuming and may result in geometrically inaccurate models. In order to address this need we have developed a technique for taking a model of the cortex, detecting and fixing the topological defects while leaving that majority of the model intact, resulting in a surface that is both geometrically accurate and topologically correct.

Estimation and detection of event-related fMRI signals with temporally correlated noise: a statistically efficient and unbiased approach

Recent developments in analysis methods for event-related functional magnetic resonance imaging (fMRI) has enabled a wide range of novel experimental designs. As with selective averaging methods used in event-related potential (ERP) research, these methods allow for the estimation of the average time-locked response to particular event-types, even when these events occur in rapid succession and in an arbitrary sequence. Here we present a flexible framework for obtaining efficient and unbiased estimates of event-related hemodynamic responses, in the presence of realistic temporally correlated (nonwhite) noise. We further present statistical inference methods based upon the estimated responses, using restriction matrices to formulate temporal hypothesis tests about the shape of the evoked responses. The accuracy of the methods is assessed using synthetic noise, actual fMRI noise, and synthetic activation in actual noise. Actual false-positive rates were compared to nominal false-positive rates assuming white noise, as well as local and global noise estimates in the estimation procedure (assuming white noise resulted in inappropriate inference, while both global and local estimates corrected false-positive rates). Furthermore, both local and global noise estimates were found to increase the statistical power of the hypothesis tests, as measured by the receiver operating characteristics (ROC). This approach thus enables appropriate univariate statistical inference with improved statistical power, without requiring a priori assumptions about the shape or timing of the event-related hemodynamic response.

Measuring the thickness of the human cerebral cortex from magnetic resonance images

Accurate and automated methods for measuring the thickness of human cerebral cortex could provide powerful tools for diagnosing and studying a variety of neurodegenerative and psychiatric disorders. Manual methods for estimating cortical thickness from neuroimaging data are labor intensive, requiring several days of effort by a trained anatomist. Furthermore, the highly folded nature of the cortex is problematic for manual techniques, frequently resulting in measurement errors in regions in which the cortical surface is not perpendicular to any of the cardinal axes. As a consequence, it has been impractical to obtain accurate thickness estimates for the entire cortex in individual subjects, or group statistics for patient or control populations. Here, we present an automated method for accurately measuring the thickness of the cerebral cortex across the entire brain and for generating cross-subject statistics in a coordinate system based on cortical anatomy. The intersubject standard deviation of the thickness measures is shown to be less than 0.5 mm, implying the ability to detect focal atrophy in small populations or even individual subjects. The reliability and accuracy of this new method are assessed by within-subject test-retest studies, as well as by comparison of cross-subject regional thickness measures with published values.

High-resolution intersubject averaging and a coordinate system for the cortical surface

The neurons of the human cerebral cortex are arranged in a highly folded sheet, with the majority of the cortical surface area buried in folds. Cortical maps are typically arranged with a topography oriented parallel to the cortical surface. Despite this unambiguous sheetlike geometry, the most commonly used coordinate systems for localizing cortical features are based on 3-D stereotaxic coordinates rather than on position relative to the 2-D cortical sheet. In order to address the need for a more natural surface-based coordinate system for the cortex, we have developed a means for generating an average folding pattern across a large number of individual subjects as a function on the unit sphere and of nonrigidly aligning each individual with the average. This establishes a spherical surface-based coordinate system that is adapted to the folding pattern of each individual subject, allowing for much higher localization accuracy of structural and functional features of the human brain.

Location of human face-selective cortex with respect to retinotopic areas

Functional Magnetic Resonance Imaging (fMRI) was used to identify a small area in the human posterior fusiform gyrus that responds selectively to faces (PF). In the same subjects, phase-encoded rotating and expanding checkerboards were used with fMRI to identify the retinotopic visual areas V1, V2, V3, V3A, VP and V4v. PF was found to lie anterior to area V4v, with a small gap present between them. Further recordings in some of the same subjects used moving low-contrast rings to identify the visual motion area MT. PF was found to lie ventral to MT. In addition, preliminary evidence was found using fMRI for a small area that responded to inanimate objects but not to faces in the collateral sulcus medial to PF. The retinotopic visual areas and MT responded equally to faces, control randomized stimuli, and objects. Weakly face-selective responses were also found in ventrolateral occipitotemporal cortex anterior to V4v, as well as in the middle temporal gyrus anterior to MT. We conclude that the fusiform face area in humans lies in non-retinotopic visual association cortex of the ventral form-processing stream, in an area that may be roughly homologous in location to area TF or CITv in monkeys.

Segregation of somatosensory activation in the human rolandic cortex using fMRI

The segregation of sensory information into distinct cortical areas is an important organizational feature of mammalian sensory systems. Here, we provide functional magnetic resonance imaging (fMRI) evidence for the functional delineation of somatosensory representations in the human central sulcus region. Data were collected with a 3-Tesla scanner during two stimulation protocols, a punctate tactile condition without a kinesthetic/motor component, and a kinesthetic/motor condition without a punctate tactile component. With three-dimensional (3-D) anatomical reconstruction techniques, we analyzed data in individual subjects, using the pattern of activation and the anatomical position of specific cortical areas to guide the analysis. As a complimentary analysis, we used a brain averaging technique that emphasized the similarity of cortical features in the morphing of individual subjects and thereby minimized the distortion of the location of cortical activation sites across individuals. A primary finding of this study was differential activation of the cortex on the fundus of the central sulcus, the position of area 3a, during the two tasks. Punctate tactile stimulation of the palm, administered at 3 Hz with a 5.88(log10.mg) von Frey filament, activated discrete regions within the precentral (PreCG) and postcentral (PoCG) gyri, corresponding to areas 6, 3b, 1, and 2, but did not activate area 3a. Conversely, kinesthetic/motor stimulation, 3-Hz flexion and extension of the digits, activated area 3a, the PreCG (areas 6 and 4), and the PoCG (areas 3b, 1, and 2). These activation patterns were observed in individual subjects and in the averaged data, providing strong evidence for the existence of a distinct representation within area 3a in humans. The percentage signal changes in the PreCG and PoCG regions activated by tactile stimulation, and in the intervening gap region, support this functional dissociation. In addition to this distinction within the fundus of the central sulcus, the combination of high-resolution imaging and 3-D analysis techniques permitted localization of activation within areas 6, 4, 3a, 3b, 1, and 2 in the human. With the exception of area 4, which showed inconsistent activation during punctate tactile stimulation, activation in these areas in the human consistently paralleled the pattern of activity observed in previous studies of monkey cortex.

Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity

Functional magnetic resonance imaging (fMRI) can provide maps of brain activation with millimeter spatial resolution but is limited in its temporal resolution to the order of seconds. Here, we describe a technique that combines structural and functional MRI with magnetoencephalography (MEG) to obtain spatiotemporal maps of human brain activity with millisecond temporal resolution. This new technique was used to obtain dynamic statistical parametric maps of cortical activity during semantic processing of visually presented words. An initial wave of activity was found to spread rapidly from occipital visual cortex to temporal, parietal, and frontal areas within 185 ms, with a high degree of temporal overlap between different areas. Repetition effects were observed in many of the same areas following this initial wave of activation, providing evidence for the involvement of feedback mechanisms in repetition priming.

Stochastic designs in event-related fMRI

This article considers the efficiency of event-related fMRI designs in terms of the optimum temporal pattern of stimulus or trial presentations. The distinction between "stochastic" and "deterministic" is used to distinguish between designs that are specified in terms of the probability that an event will occur at a series of time points (stochastic) and those in which events always occur at prespecified time (deterministic). Stochastic designs may be "stationary," in which the probability is constant, or nonstationary, in which the probabilities change with time. All these designs can be parameterized in terms of a vector of occurrence probabilities and a prototypic design matrix that embodies constraints (such as the minimum stimulus onset asynchrony) and the model of hemodynamic responses. A simple function of these parameters is presented and used to compare the relative efficiency of different designs. Designs with slow modulation of occurrence probabilities are generally more efficient than stationary designs. Interestingly the most efficient design is a conventional block design. A critical point, made in this article, is that the most efficient design for one effect may not be the most efficient for another. This is particularly important when considering evoked responses and the differences among responses. The most efficient designs for evoked responses, as opposed to differential responses, require trial-free periods during which baseline levels can be attained. In the context of stochastic, rapid-presentation designs this is equivalent to the inclusion of "null events."